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Retinal neovascularization as self-organized criticality on ultra-widefield fluorescein angiography imaging of diabetic retinopathy

Eye volume 37, pages 2795–2800 (2023)Cite this article

Subjects

Abstract

Background/Objectives

Do the distributions of surface area of non-perfusion (NP) and neovascularization (NV) on ultra-widefield fluorescein angiography (UWF FA) in patients with diabetic retinopathy (DR) differ significantly?

Subjects/Methods

Inclusion criteria were patients who had a UWF FA taken for DR at the Kellogg Eye Center from January 2009 to May 2018. Exclusion criteria included previous panretinal photocoagulation and significant media opacity (e.g., vitreous haemorrhage or significant cataract). UWF FAs were manually segmented for surface areas of NP and NV. The total areas per patient were organized in a histogram, and logarithmically binned to test against power law and exponential distributions. Then, a computational model was constructed in Python 3.7 to suggest a mechanistic explanation for the observed distributions.

Results

Analysis of areas of NV across 189 images demonstrated a superior fit by the least squares method to a power law distribution (p = 0.014) with an R2 fit of 0.9672. Areas of NP over 794 images demonstrated a superior fit with an exponential distribution instead (p = 0.011). When the far periphery was excluded, the R2 fit for the exponential distribution was 0.9618. A computational model following the principles of self-organized criticality (SOC), akin to earthquake and forest fire models, matched these datasets.

Conclusions

These distributions inform what useful statistics may be applied to study of these imaging characteristics. Further, the difference in event distribution between NV and NP suggests that the two phenomena are mechanistically distinct. NV may follow SOC, propagating as a catastrophic event in an unpredictable manner.

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Fig. 1: Diabetic retinal neovascularization areas by frequency over 189 patients with retinal neovascularization.
Fig. 2: Diabetic retinal non-perfusion areas by frequency over 794 patients.
Fig. 3: Diabetic retinal non-perfusion areas by frequency, with far peripheral areas excluded with the assumption that the far periphery was most subject to noise, such as from lash artefact and image distortion.
Fig. 4: A computational simulation of retinal neovascularization.

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Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request, pending ethical approval.

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Acknowledgements

The authors would also like to thank Dave Musch, PhD and Marta Gilson, PhD who are both affiliated with the University of Michigan for their insightful discussion and preliminary univariate statistical analyses.

Funding

This work was supported by the National Eye Institute grant 1K08EY027458, 1R01EY033000, and 1R41EY031219 (YMP), the University of Michigan Department of Ophthalmology and Visual Sciences, unrestricted departmental support from Research to Prevent Blindness, generous support of the Helmut F. Stern Career Development Professorship in Ophthalmology and Visual Sciences (YMP), and the Heed Ophthalmic Foundation. These funding organizations were not involved with the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

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Authors and Affiliations

  1. Department of Ophthalmology and Visual Sciences, W.K. Kellogg Eye Center, University of Michigan Medical School, Ann Arbor, MI, USA

    Benjamin K. Young, Nikhil Bommakanti, Gina Yu, Tapan P. Patel, Lyna Azzouz, Corey Powell & Yannis M. Paulus

  2. Department of Ophthalmology, Byers Eye Institute, Stanford University School of Medicine, Palo Alto, CA, USA

    Gina Yu

  3. Wilmer Eye Institute, Johns Hopkins University, Baltimore, MD, USA

    Tapan P. Patel

  4. Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA

    Yannis M. Paulus

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Contributions

GY, TPP and YMP obtained ethical approval. GY, LA and TPP collected data. GY, TPP, LA, NB and BKY performed data analysis. CP performed statistical analysis. BKY and NB wrote the main manuscript text. YMP provided supervision and revised the manuscript. All listed authors have approved the submitted version of the manuscript.

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Correspondence to Yannis M. Paulus.

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Young, B.K., Bommakanti, N., Yu, G. et al. Retinal neovascularization as self-organized criticality on ultra-widefield fluorescein angiography imaging of diabetic retinopathy. Eye 37, 2795–2800 (2023). https://doi.org/10.1038/s41433-023-02422-1

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